3.2 KiB
3.2 KiB
title | id | challengeType | forumTopicId |
---|---|---|---|
Ethiopian multiplication | 599d1566a02b571412643b84 | 5 | 302257 |
Description
- Take two numbers to be multiplied and write them down at the top of two columns
- In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last in the same column, until you write a value of
1
- In the right-hand column repeatedly double the last number and write the result below. stop when you add a result in the same row as where the left hand column shows
1
- Examine the table produced and discard any row where the value in the left column is even
- Sum the values in the right-hand column that remain to produce the result of multiplying the original two numbers together
17 × 34
17 34Halving the first column:
17 34 8 4 2 1Doubling the second column:
17 34 8 68 4 136 2 272 1 544Strike-out rows whose first cell is even:
17 34 8Sum the remaining numbers in the right-hand column:68413622721 544
17 34 8 -- 4 --- 2 --- 1 544 ==== 578So
17
multiplied by 34
, by the Ethiopian method is 578
.
Instructions
- one to halve an integer,
- one to double an integer, and
- one to state if an integer is even
Tests
tests:
- text: <code>eth_mult</code> is a function.
testString: assert(typeof eth_mult === 'function');
- text: <code>eth_mult(17,34)</code> should return <code>578</code>.
testString: assert.equal(eth_mult(17, 34), 578);
- text: <code>eth_mult(23,46)</code> should return <code>1058</code>.
testString: assert.equal(eth_mult(23, 46), 1058);
- text: <code>eth_mult(12,27)</code> should return <code>324</code>.
testString: assert.equal(eth_mult(12, 27), 324);
- text: <code>eth_mult(56,98)</code> should return <code>5488</code>.
testString: assert.equal(eth_mult(56, 98), 5488);
- text: <code>eth_mult(63,74)</code> should return <code>4662</code>.
testString: assert.equal(eth_mult(63, 74), 4662);
Challenge Seed
function eth_mult(a, b) {
// Good luck!
}
Solution
function eth_mult(a, b) {
let sum = 0; a = [a]; b = [b];
let half = a => a / 2,
double = a => a * 2,
is_even = a => a % 2 == 0;
while (a[0] !== 1) {
a.unshift(Math.floor(half(a[0])));
b.unshift(double(b[0]));
}
for (let i = a.length - 1; i > 0; i -= 1) {
if (!is_even(a[i])) {
sum += b[i];
}
}
return sum + b[0];
}